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Sample Size and Power Calculations |

The power for the one-way ANOVA is computed in a similar
manner as for the hypothesis tests. That is, power is the
probability of correctly
rejecting the null (all group means are equal) in favor
of the alternative hypothesis (at least one group mean is not
equal), when the alternative is true.
The sample size is the number per group; these calculations assume
equally sized groups. To compute the power, you make
use of the noncentral *F* distribution. The formula
(O'Brien and Lohr 1984) is given by

where *F* is distributed as the noncentral and is the
() quantile of the *F* distribution with and degrees of freedom.

- is the numerator df
- is the denominator df
*n*- is the number per group
*r*- is the number of groups
- is the noncentrality parameter
- is the corrected sum of squares
- is the mean of the
*g*th group - is the overall mean
- is estimated by the mean squared error (MSE)

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